What's the Effect of Resistance on the Efficiency of a Lamp?

📌 CONCEPT: The efficiency of a lamp is directly proportional to its resistance, as per the given information.

📐 RULE / FORMULA: The power consumed by a device is given by the formula P = V^2/R, where P is the power, V is the supply voltage, and R is the resistance.

💡 WORKED EXAMPLE: Given a 100 W light bulb with a resistance of 10 Ω, if the power consumed increases to 110 W and the supply voltage remains the same, we can calculate the new resistance using the formula R = V^2/P. Solving for R, we get R = 10.909 Ω. Since the efficiency is directly proportional to resistance, the increase in power will lead to a decrease in efficiency.

⚠️ COMMON MISTAKE: Students might assume that an increase in power consumption directly translates to an increase in efficiency, which is not the case here, as the efficiency is directly proportional to the resistance.